We construct a compactification $M^{ \mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma \colon M^{ ss} \to M^{ \mu ss}$, where $M^{ ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{ \mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.
Categories: math.AG math-ph math.DG math.MP